Science > Physics > This Week's Finds in Mathematical Physics (Week 214)
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Science > Physics |
| User: |
"John Baez" |
| Date: |
21 Apr 2005 04:27:49 PM |
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This Week's Finds in Mathematical Physics (Week 214) |
Also available at http://math.ucr.edu/home/baez/week214.html
April 15, 2005
This Week's Finds in Mathematical Physics - Week 214
John Baez
What common English slang phrase alludes to the number 168?
I won't tell you - not right away. But, I'll tell you a bunch of
other cool stuff about this number, and eventually the answer should
jump out at you.
Okay:
Start with a bunch of equilateral triangles. Glue them together
so that 3 meet at each corner. You get a regular tetrahedron.
Next, take a bunch of squares. Glue them together so that 3
meet at each corner. You get a cube.
Next, take a bunch of regular pentagons. Glue them together so
that three meet at each corner. You get a regular dodecahedron.
This is fun! We're getting a series of Platonic solids.
Next, take a bunch of regular hexagons and glue them together
so that three meet at each corner. Now the angles of the hexagons
add up to 360 degrees, so we don't get a Platonic solid. Instead, we
get a tiling of the plane. It looks like a honeycomb that stretches
out forever in all directions.
But, if you want something finite in size, you can cut out a portion
of this honeycomb and curl it up to get a doughnut, or torus. There
are actually lots of ways to do this. You might have fun figuring out
what they all are. Can you take just *one* regular hexagon and curl
it up to form a torus?
Anyway, these tori deserve to be called "Platonic surfaces", since
they are surfaces tiled with regular polygons, with the same number
meeting at each vertex.
Next, let's take a bunch of regular *heptagons* and glue them
together so that three meet each corner. Now the angles add up
to more than 360 degrees, so we get a tiling of the "hyperbolic
plane". The hyperbolic plane is like the opposite of a sphere,
since it's saddle-shaped at every point instead of bulging
out at every point. In fact the sphere and the hyperbolic plane
are the two most symmetrical forms of non-Euclidean geometry.
The sphere is "positively curved", while the hyperbolic plane is
"negatively curved".
You may have trouble visualizing the hyperbolic plane tiled with
regular heptagons, but if we distort it, it fits into a disk and
looks really pretty! Here it is:
1) Don Hatch, picture of {7,3},
http://www.hadron.org/~hatch/HyperbolicTesselations/7_3_trunc0_512x512.gif
It's called "{7,3}", since it's made of 7-sided figures with 3
meeting at each corner.
In this picture there's one heptagon at the center, surrounded by
rings of heptagons that appear smaller (but aren't really - that's
just an effect of the distortion).
Can we cut out a portion of this tiling and curl it up to get
a torus? No! But, we can curl up a portion to get a 3-holed
torus - like the surface of a doughnut with three holes. But,
we can only do this if we use precisely 24 heptagons!
Here's how we do it. Here's a picture of 24 heptagons, taken
from an old paper by Klein and Fricke but prettied up a bit:
2) Tony Smith, Klein's quartic surface,
http://www.valdostamuseum.org/hamsmith/Klein168.gif
You'll notice they're drawn in a fancy style: each heptagon has
been "barycentrically subdivided" into 14 right triangles.
But don't worry about that yet; concentrate on the heptagons.
There's a blue heptagon in the middle, 7 red ones touching that
7 yellow ones touching those, then 7 green ones falling off the
edge of the picture, and one blue one that's broken into bits all
around the corners of the picture. That's a total of 24 heptagons.
We wrap this thing up into a 3-holed torus using the numbers on
the edges of the picture:
connect edges 1 and 6
connect edges 3 and 8
connect edges 5 and 10
connect edges 7 and 12
connect edges 9 and 14
connect edges 11 and 2
connect edges 13 and 4
To connect them in the correct way, make sure that triangles
of the same color never touch each other.
Here's how to see if get the idea. Ignore the little
triangles; just pay attention to the heptagons! Then:
Start on any edge of any heptagon and march along in either direction.
Then, when you get to the end, turn left.
Then, when you get to the end, turn right.
Then, when you get to the end, turn left.
Then, when you get to the end, turn right.
Then, when you get to the end, turn left.
Then, when you get to the end, turn right.
Then, when you get to the end, turn left.
Then, when you get to the end, turn right.
You should now be back where you started!!!
These are like the driving directions the devil gives people who ask
the way out of hell. LRLRLRLR and you're right back where you started.
But the resulting Platonic surface is heavenly. It has lots of
symmetries. Each of the 24 heptagons has 7-fold rotational symmetry -
and amazingly, all these rotations extend to a symmetry of the Platonic
surface!
Moreover, if you do any of these rotations and then do another
one centered at some other heptagon, you get *another* rotation
centered at *another* heptagon. So, our Platonic surface has a
symmetry group with
7 x 24 = 168
elements! These are all the symmetries except for reflections. If
we include reflections, the symmetry group has size
168 x 2 = 336.
Now let's talk about those little triangles. Since our surface
is made of 24 heptagons, each chopped into 14 right triangles,
there are a total of
24 x 14 = 336
triangles. This is just the number of symmetries!
This is no coincidence. We can specify a symmetry by saying where
it sends our favorite right triangle. Since it can go to any other
triangle, there are 336 possibilities.
By the way, this trick works for ordinary Platonic solids as well.
For example, if we take a dodecahedron and barycentrically subdivide
all 12 pentagons, we get 10 x 12 = 120 right triangles. If we pick
one of these as the "identity element", we can specify any symmetry by
saying which triangle this triangle gets sent to. So, the set of
triangles becomes a vivid PICTURE of the 120-element symmetry group of
the dodecahedron. It's called the "Coxeter complex". This idea
generalizes in many directions, and is incredibly useful.
Anyway... there is much more to say about this stuff. For example,
if we take our hyperbolic plane tiled with heptagons and count them
grouped according to how far they are from the central one, we get
the sequence
7, 7, 14, 21, 35, 56, 91, ....
These are 7 times the Fibonacci numbers!
To dig a bit deeper, though, it helps to think about complex analysis.
If we think of the hyperbolic plane as the unit disc in the complex
plane, this surface becomes a "Riemann surface", meaning that it
gets equipped with a complex structure. This was Felix Klein's
viewpoint when he discovered all this stuff in about 1878. He
showed this surface could be described by an incredibly symmetrical
quartic equation in 3 complex variables:
u^3 v + v^3 w + w^3 u = 0
where we count two solutions as the same if they differ by an overall
factor. So, it's called "Klein's quartic curve".
(Why a "curve" and not a surface? Because it takes one *complex*
number to say where you are on it. We have 3 unknowns and one
equation, but we mod out by an overall factor, so we get something
locally parametrized by one complex number... so algebraic geometers
call it a curve.)
You can read Klein's original article translated into English.
It's available online as part of a whole *book* about his incredible
quartic:
3) Silvio Levy, The Eightfold Way: the Beauty of Klein's Quartic Curve,
MSRI Research Publications 35, Cambridge U. Press, Cambridge 1999.
Review available at http://www.msri.org/publications/books/Book35/
This book was put out by the Mathematical Sciences Research Institute
in Berkeley, to celebrate the completion of sculpture of Klein's
quartic curve made by Helaman Ferguson. I must admit that the
sculpture leaves me unmoved. But the curve itself - ah, that's
another story!
For example, Klein's quartic curve turns out to have the maximum
number of symmetries of any 3-holed Riemann surface.
Let's back up a minute and think about a Riemann surface with no holes:
a sphere. There's only one way to make a sphere into a Riemann
surface - it's called the Riemann sphere. You can think of it as
the complex numbers plus a point at infinity. This has *infinitely*
many symmetries. They're called conformal transformations, and they
all look like this:
az + b
z |---> --------
cz + d
They form a group called PSL(2,C), since it's the same as the group of
2x2 complex matrices with determinant 1, mod scalars. It's also the
same as the Lorentz group!
There are different ways to make a torus into a Riemann surface,
some with more symmetries than others (see "week124"). But, there
are always translation symmetries in both directions, so the symmetry
group is always infinite.
On the other hand, a Riemann surface with 2 or more holes can only
have a *finite* group of conformal transformations. In fact, in 1893
Hurwitz proved that a Riemann surface with g holes has at most
84(g - 1)
For g = 2, this is 168. So, Klein's quartic surface is as symmetrical
as possible! (We don't count reflections here, since they don't
preserve the complex structure - they're like complex conjugation.)
Now I should break down and give the best description of Klein's
quartic curve as a Riemann surface. Sitting inside PSL(2,C) is
PSL(2,Z), where we only use integers a,b,c,d in our fractional linear
transformation
az + b
z |---> --------
cz + d
This subgroup acts on the upper half-plane H, which is just another
way of thinking about the hyperbolic plane.
Sitting inside PSL(2,Z) is a group Gamma(7) consisting of guys where
the matrix
a b
c d
is congruent to the identity:
1 0
0 1
modulo 7. This is an example of a "congruence subgroup"; these serve
to relate complex analysis to number theory in lots of cool ways.
In particular, Klein's quartic curve is just
H/Gamma(7)
Since Gamma(7) is a normal subgroup of PSL(2,Z), the quotient
group
PSL(2,Z)/Gamma(7) = PSL(2,Z/7)
acts as symmetries of Klein's quartic curve. And, this group has
168 elements!
In fact, this group is the second smallest simple group. The
smallest one is the rotational symmetry group of the icosahedron,
which has 60 elements. This group is actually PSL(2,Z/5), and
Klein had run into it in his work on the icosahedron and
quintic equations (see "week213"). So, it's actually far from
sheer luck that he then moved on to PSL(2,Z/7) and ran into his
wonderful quartic curve.
By the way, this 168-element group is also known as PSL(3,Z/2) -
the symmetry group of the "Fano plane". This is a name for the
projective plane over Z/2. The Fano plane is closely related to
the octonions:
3) John Baez, The Fano plane,
http://math.ucr.edu/home/baez/octonions/node4.html
So in fact, our 168-element group acts on the set of octonion
multiplication tables:
4) Tony Smith, Octonion products,
http://www.valdostamuseum.org/hamsmith/480op.html
5) Geoffrey Dixon, Octonion multiplication tables,
http://www.7stones.com/Homepage/octotut0.html
And, as James Dolan just noted today, and Tony Smith seems to have known
all along, there's a way to draw the Fano plane that even LOOKS like
the diagram Klein and Fricke used to build the Klein quartic.
So, something interesting is going on, and I want to know what it is!
By the way, fans of the quaternions and octonions may like this
review of Conway and Smith's book:
6) John Baez, review of "On Quaternions and Octonions: Their Geometry,
Arithmetic and Symmetry", by John H. Conway and Derek A. Smith,
Bull. Amer. Math. Soc. 42 (2005), 229-243. Available at
http://www.ams.org/bull/2005-42-02/ and
http://math.ucr.edu/home/baez/octonions/node24.html
It's packed with cool pictures and weird facts - a more refined
version of the material in "week193" and "week194".
It builds up to a kind of crazy climax in which I describe how when you
pack spheres as densely as possible in 8 dimensions, each sphere touches
240 others... and if you look at the 240 neighbors of a given sphere, each
one of those neighbors touches 56 other neighbors. Then I explain how this
gives rise to a 56-dimensional manifold on which the exceptional group E8
acts - the smallest space on which it acts nontrivially! And, how it
gives rise to a 57-dimensional representation of the exceptional group E7 -
its smallest nontrivial representation!
Bertram Kostant is one of the real gurus of Lie theory. He teaches at
MIT, and he has a strong fondness for exceptional Lie groups. When he saw
this review of mine, he mentioned a couple of other papers that construct
the 56-dimensional space on which E8 acts:
7) Ranee Brylinski and Bertram Kostant, Lagrangian models of minimal
representations of E6, E7, and E8, in Functional Analysis on the Eve
of the 21st Century, vol. 1, Progress in Math. 131, Birkhauser, Boston,
1995, pp. 13-53.
Bertram Kostant, Minimal coadjoint orbits and symplectic induction,
in The Breadth of Symplectic and Poisson geometry, 391-422,
Progress in Math. 232, Birkhauser, Boston, 2005. Also
available as math.SG/0312252.
I've got to read these sometime.
Having the number 56 on my brain, I can't resist nothing that if
you take Klein's quartic curve tiled by heptagons, and you count
the vertices, you get
24 x 7 / 3 = 56
since each vertex is shared by 3 heptagons. I'm hoping this is
not a coincidence!
Okay, that's all for this week, except for some silly stuff....
First of all, speaking of octonions, Geoff Corbishley just told me
that their inventor, John Thomas Graves, is a relative of Robert
Graves - the author of "I Claudius".
Second of all, I hope you've figured out the puzzle I gave at the
beginning of this Week. The phrase is "24-7", as in "we're working
on it 24-7". 24 hours a day, 7 days a week, makes 168 hours per week!
Finally, speaking of numerology, this number 168 is related to why the
days of the week have the names they do! I explained why in "week175",
but I'll remind you:
Astrologers liked to list the planets in order of decreasing orbital
period, counting the sun as having a period of one year, and the moon
as period of one month:
Saturn (29 years)
Jupiter (12 years)
Mars (687 days)
Sun (365 days)
Venus (224 days)
Mercury (88 days)
Moon (29.5 days)
For the purposes of astrology they wanted to assign a planet to each
hour of each day of the week. To do this, they assigned Saturn to
the first hour of the first day, Jupiter to the second hour of the
first day, and so on, cycling through the list of planets over and
over, until each of the 24 x 7 = 168 hours was assigned a planet.
Each day was then named after the first hour in that day. Since
24 mod 7 equals 3, this amounts to taking the above list and cycling
around it, reading off every third planet:
Saturn (Saturday)
Sun (Sunday)
Moon (Monday)
Mars (Tuesday)
Mercury (Wednesday)
Jupiter (Thursday)
Venus (Friday)
And that's how they got listed in this order! At least, this is what
the Roman historian Dion Cassius (AD 150-235) claims. Nobody knows for
sure.
-----------------------------------------------------------------------
Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained at
http://math.ucr.edu/home/baez/
For a table of contents of all the issues of This Week's Finds, try
http://math.ucr.edu/home/baez/twf.html
A simple jumping-off point to the old issues is available at
http://math.ucr.edu/home/baez/twfshort.html
If you just want the latest issue, go to
http://math.ucr.edu/home/baez/this.week.html
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| User: "John Baez" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 214) |
22 Apr 2005 08:49:59 PM |
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I made some mistakes, which I have fixed in the web version:
http://math.ucr.edu/home/baez/week214.html
2) Tony Smith, Klein's quartic surface,
http://www.valdostamuseum.org/hamsmith/Klein168.gif
There's a blue heptagon in the middle, 7 red ones touching that
7 yellow ones touching those, then 7 green ones falling off the
edge of the picture, and one blue one that's broken into bits all
around the corners of the picture. That's a total of 24 heptagons.
As some folks noticed, 1 + 7 + 7 + 7 + 1 = 23. There are
actually 2 blue heptagons broken into bits all around the
corners of the picture.
You can read Klein's original article translated into English.
It's available online as part of a whole *book* about his incredible
quartic:
3) Silvio Levy, The Eightfold Way: the Beauty of Klein's Quartic Curve,
MSRI Research Publications 35, Cambridge U. Press, Cambridge 1999.
Review available at http://www.msri.org/publications/books/Book35/
In fact the whole book is available here:
http://www.msri.org/publications/books/Book35/
It builds up to a kind of crazy climax in which I describe how when you
pack spheres as densely as possible in 8 dimensions, each sphere touches
240 others... and if you look at the 240 neighbors of a given sphere, each
one of those neighbors touches 56 other neighbors. Then I explain how this
gives rise to a 56-dimensional manifold on which the exceptional group E8
acts - the smallest space on which it acts nontrivially! And, how it
gives rise to a 57-dimensional representation of the exceptional group E7 -
its smallest nontrivial representation!
Actually the manifold is 57-dimensional, and the representation is
56-dimensional.
Also, the 60- and 168-element groups are the two smallest
*nonabelian* simple groups.
.
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| User: "Traveler" |
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| Title: Re: This Week's Finds in Mathematical Physics (Week 214) |
21 Apr 2005 05:40:03 PM |
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In article <d47atp$6qr$1@glue.ucr.edu>,
baez@math.removethis.ucr.andthis.edu (John Baez) wrote:
Also available at http://math.ucr.edu/home/baez/week214.html
April 15, 2005
This Week's Finds in Mathematical Physics - Week 214
John Baez
What common English slang phrase alludes to the number 168?
I won't tell you - not right away. But, I'll tell you a bunch of
other cool stuff about this number, and eventually the answer should
jump out at you.
Okay:
Start with a bunch of equilateral triangles. Glue them together
so that 3 meet at each corner. You get a regular tetrahedron.
Next, take a bunch of squares. Glue them together so that 3
meet at each corner. You get a cube.
Next, take a bunch of regular pentagons. Glue them together so
that three meet at each corner. You get a regular dodecahedron.
This is fun! We're getting a series of Platonic solids.
The resident grown-up nerd has struck again. Physics is all about
puzzles and fun and wonderfully complicated little things for Baez.
Anything to show off how smart he is.
Tell me Baez, why causes a moving body to remain in motion? Years ago,
you wrote on sci.physics that it is the metrics of spacetime that
keeps bodies in motion. Could you run that by me again?
Louis Savain
The Silver Bullet: Why Software Is Bad and What We Can Do to Fix it
http://users.adelphia.net/~lilavois/Cosas/Reliability.htm
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
22 Apr 2005 10:03:33 PM |
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Louis ..168 must be how many joints he smoked writing it.
F is identical to the gain ( change ) in mass stupid. not all the atom
is F .
=A0=A0F is a % of the mass .
V is constant just because all the atoms gained the same % of thier
mass.
F is identical to G as the gain in mass from one side of evry atom to
the other.
=A0=A0UP is a gain in mass .
a scale does measue the gain .
=A0=A0It just so happends the math is identical. F is the gain in *****
and V allways comes out the same .
=A0=A0=A0=A0That's the pice of math Einstein longed for. The unification
of the two.
It;s no theroretical idia ..it's just identical .
F is the gain in mass pushing the atom to less mass . =A0 V is constant
because evry atoms F is perportional to the mass .
=A0=A0Very simple observation after you understand it.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 04:09:32 AM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:27176-4269BB05-229@storefull-3214.bay.webtv.net...
<snip nonsense>
By the way I am still waiting for your "goons" to come round
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 10:25:02 AM |
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1 ,, T wake's phd went down the tolet.
2 . T wake cant controle himself in fron of a class that knows how to
punch his knobs .
3. T wake dont know what the speed of all the stars are , so drawing a
universe without that is imposible.
4 .. T wakes studdy methods dont make the grade. and you a teacher.
5 , T wake failed to answer basic physics questions corectly.
6 . T wake's ignorance or racial brainwashing has caused him to think
engish people are smarter than asian people.
What fucked up school did you come from ?
Flag waving idiots fail to studdy history and are doomed to repeat it.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 01:54:03 PM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:18295-426A68CE-235@storefull-3215.bay.webtv.net...
1 ,, T wake's phd went down the tolet.
You are entitled to your opinion.
2 . T wake cant controle himself in fron of a class that knows how to
punch his knobs .
I doubt this is true although I have never tested it as I dont teach
anything to classes of people who know how to punch my "knobs."
I must admit I admire your ability to stay true to your delusions about my
profession.
3. T wake dont know what the speed of all the stars are , so drawing a
universe without that is imposible.
Nonsense.
4 .. T wakes studdy methods dont make the grade. and you a teacher.
I never, ever said I was a teacher. This is something you have made up.
5 , T wake failed to answer basic physics questions corectly.
Not true. Your confusion over mass and weight means you refuse to accept
anything except your own tortured beliefs.
6 . T wake's ignorance or racial brainwashing has caused him to think
engish people are smarter than asian people.
Also not true. Where did you get this from. You have no idea of my ethnic
origin or you wouldnt even come close to saying this.
What fucked up school did you come from ?
Flag waving idiots fail to studdy history and are doomed to repeat it.
tj - until recently you have been mildly amusing. Your lack of coherence and
inability to reason or comprehend simple things, combined with your
narcissistic fantasies makes this no longer the case.
Its a shame because you did entertain me for a while. Now I think you are a
sad lonely person who genuinely needs some comfort and help from a community
care provider.
I am still waiting for your "goons" to turn up. Tomorrow I will probably be
sitting in the front garden for most of the day. You should be able to find
me easily enough.
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 02:44:32 PM |
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Wake ,,
The question is still "How does gravity move anything ".
You still have not posted te speed of the stars or the speed of the
rotoation of the universe.
I dont have any beliefs ,,,The gain in mass and bent space is all
einsten's idia.
It's Einstein's gravity idias not mine .
Up is a gain in mass and is measured on a scale as a fact.
Evry atom gained it's own identical perportion.
The mass left to fall will fall twards less mass down .
Nothing is pulling the atom down .
The atom is pushing it's self down the slope.
Its in bent space ,,to say an energy gradiant.
A slope from one side of the atom to the other.
An atom in motion is in a slope afecting how much mass is where inside
the atom.
EMF is allso affecting the orbital time and slope .
KE . G . EMF ..all affect the slope accross the atom.
The atoms parts change mass at C ,,another fact and not my idia.
F is identical to the gain in mass pushing the rest of the mass of
the atom,\=A9=A1=A9=97=97
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 03:07:24 PM |
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post 4 other T Wakes in your time zone ..
or as a matter of fact your the only T wake in BC and usa and peru.
no T wake in UK .
show me 4 T Wake .
one with your identical writing .
All your doing is bitching ,, you might try some facts .
I say the stars have all gone 180 million light years based on the
speeds we know they travel.
And the dark energy we measure with BGR shows the speed of the
universe ege .
You stem to think thats a dillusional conjob.
You fail to discuss gravity at all.
Your more conserned about goons .
I dont remeber the crackerjack box with a post hole digger inside =BF
The philosophies of physical sciences.
You grew up in a world ,not ,,but in a small pice of it with a very
narow view.
I grew up in another world with orther views.
I know people in mi that think people from KY are hillbillies.
Evry place I go they think they are better than evryone else.
Post hole diggers ,,evry one of the basterds.
38 MW AC driven by a sliding vane hyydrolic motor for water from a 28
inch pipe 5 miles long going up 1500 feet is no the dumb toy you might
think it is.
maybe you hink rich people all spell harvord.
russkies are a bit dumber than the amercans dont you think
??????????????????????
if anything biult in china was worth a ***** usa would disapear
overnight .
is this the way you think ????
You might be a dumbass .
How much does a dumbass make a year ??
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 03:32:08 PM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:4085-426AAAFC-36@storefull-3212.bay.webtv.net...
post 4 other T Wakes in your time zone ..
or as a matter of fact your the only T wake in BC and usa and peru.
no T wake in UK .
---
Nonsense. However feel free to belive it. I am sure if you knew how to
search internet phone books you would realise your mistake here.
Like most things though you consistently fail to accept when you are
mistaken.
---
show me 4 T Wake .
one with your identical writing .
---
Whatever.
---
All your doing is bitching ,, you might try some facts .
I say the stars have all gone 180 million light years based on the
speeds we know they travel.
---
If you think I am bitching then I am sorry. I am not. However, things may
appear differently in your reality.
Your assertations and assumptions are incorrect.
---
And the dark energy we measure with BGR shows the speed of the
universe ege .
---
Again you are making incorrect assumptions.
---
You stem to think thats a dillusional conjob.
You fail to discuss gravity at all.
Your more conserned about goons .
---
You started it with threatening to send your henchmen round to sort me out.
I have never tried to assert that anything is delusional other than most of
your posts.
I will discuss gravity with someone who understands the difference between
mass and weight.
---
I dont remeber the crackerjack box with a post hole digger inside ¿
---
Good one. I will laugh at this for weeks. How do you come up with material
like this?
---
The philosophies of physical sciences.
You grew up in a world ,not ,,but in a small pice of it with a very
narow view.
I grew up in another world with orther views.
I know people in mi that think people from KY are hillbillies.
Evry place I go they think they are better than evryone else.
Post hole diggers ,,evry one of the basterds.
---
I truly suspect you did grow up in another world. I fail to see how relevant
this is. I dont think I am better than anyone else. I just think you are
wrong and fairly delusional.
---
<snip ramblings>
.
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 04:03:32 PM |
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You still refuse to post any facts .
You have been reduced to explaining nothing .
No one gives a flying ***** whom you are .
There is NOT 2 T WAKE's in the world directory .
There is only 1 on the entire planet .
you still refues to tell us a thing about gravity.
Do you like lakes ?
LandAndFarm.com - Land for Sale - Township 19: - 23384 ACRES - COUNTY,
Maine, United States
Address:http://www.landandfarm.com/lf/s/63/65636.asp
Ill just make thecheck out for 12 millin.
.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 04:18:51 PM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:4084-426AB824-227@storefull-3212.bay.webtv.net...
You still refuse to post any facts .
Here is a fact: there are more than 2 T Wakes in the world.
Here is another F=ma is the formula for acceleration not gravity.
Here is another kilogrammes are a unit of mass. Newtons are a unit of
weight.
Here is another mass is not the same thing as weight. Mass remains the same
no matter what the gravitational strength is.
You have been reduced to explaining nothing .
You have never even made it to that level. You claim to explain things by
posting semi-irrelevant formula.
No one gives a flying ***** whom you are .
I dont mind.
There is NOT 2 T WAKE's in the world directory .
There is only 1 on the entire planet .
You wish.
you still refues to tell us a thing about gravity.
What more can I tell you. You refuse to listen.
Do you like lakes ?
LandAndFarm.com - Land for Sale - Township 19: - 23384 ACRES - COUNTY,
Maine, United States
Address:http://www.landandfarm.com/lf/s/63/65636.asp
Ill just make thecheck out for 12 millin.
Need I say more.
.
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
23 Apr 2005 11:22:18 PM |
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Mass is not the same in a gravity slope.
You flunked physics again.
The mass of a body is never constant but veries with the energy of the
mass .
A mass put up 1000 feet gained mass .
And THERE is just 1 T Wake on the planet.
You still can't find 4 T Wakes to post.
4 T wakes dont exsist.
Only 1 T wake ..you.
F--ma ..you still refuse to understand F is identical to the gain in
mass .
V will allways be the same.
You dont understand UP is a gain in mass .
Where did you get a PHD ???????
The mass of a neutron changes mass at C wile in orbit . In an energy
slope it will have more mass at the top of the orbit than when at the
botom of the orbit.
So the neutron is more mass falling to the center of the atom when on
the top 1/2 of the atom than the bottom 1/2 and thats what pushes the
atom to less mass.
Do you understand how Einsteins gravity works ? Not many physicsist
do.
99.9 % of PHD's dont .
.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 02:13:02 AM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:4085-426B1EFA-46@storefull-3212.bay.webtv.net...
Mass is not the same in a gravity slope.
You flunked physics again.
The mass of a body is never constant but veries with the energy of the
mass .
A mass put up 1000 feet gained mass .
Prove this. I have done a simple experiment and stood on a chair here. My
mass remained the same.
And THERE is just 1 T Wake on the planet.
You still can't find 4 T Wakes to post.
4 T wakes dont exsist.
Only 1 T wake ..you.
Ok. You are welcome to your belief. I truly hope there is only one tj Frazir
on the planet.
F--ma ..you still refuse to understand F is identical to the gain in
mass .
F=ma requires mass to remain a constant.
V will allways be the same.
You dont understand UP is a gain in mass .
You dont understand it isnt.
Where did you get a PHD ???????
Why are you asking this. You have fully identified who I am. Why would you
care.
The mass of a neutron changes mass at C wile in orbit . In an energy
slope it will have more mass at the top of the orbit than when at the
botom of the orbit.
So the neutron is more mass falling to the center of the atom when on
the top 1/2 of the atom than the bottom 1/2 and thats what pushes the
atom to less mass.
Do you understand how Einsteins gravity works ? Not many physicsist
do.
99.9 % of PHD's dont .
Ok. You are the exception to the rule I take it? No one else but you can
understand it...... Doesn't that tell you something.
By the way, going back to your previous threads where you were either going
to come round and kill me yourself or get your henchmen to do it; its a nice
sunny day outside here so I will (as planned) be sitting in the garden
waiting for you.
.
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 11:37:01 AM |
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You gained mass when you got up on the chair.
You flunked basic physics.
Your a newbee here or anywhere in physics.
Up is a gain in mass and is basic physics .
Your calling me dilusional ,,about the fact you are the only T Wake ..
you cant post 4 T Wake's if you include your self. So you call me
dilusional to try hiding the fact ..hay dumbass dont even try insisting
there are more than 1 T Wake unless you can prove it and dont try
DILLUSIONAL name calling I wount be intimadated. Your attmt to cover
your crap up by acting as stupid as moron max wount work .. You must
think I don't know what Im talking about and you think scocal
intimadation can make you look smart when you have no clue.
Your twice busted ..you cant post 4 T Wakes .
You can't post any facts about physics because you don't know basic
physics.
Re: This Week's Finds in Mathematical Physics Louis
Group: sci.physics Date: Sun, Apr 24, 2005, 8:13am (EDT+5) From:
taswakeAt@hotmail.com (T=A0Wake)
"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:4085-426B1EFA-46@storefull-3212.bay.webtv.net...
Mass is not the same in a gravity slope. You flunked physics again.
=A0=A0The mass of a body is never constant but veries with the energy of
the mass .
=A0=A0=A0=A0A mass put up 1000 feet gained mass .
Prove this. I have done a simple experiment and stood on a chair here.
My mass remained the same.
And THERE is just 1 T Wake on the planet. You still can't find 4 T Wakes
to post.
4 T wakes dont exsist.
Only 1 T wake ..you.
Ok. You are welcome to your belief. I truly hope there is only one tj
Frazir on the planet.
F--ma ..you still refuse to understand F is identical to the gain in
mass .
F=3Dma requires mass to remain a constant.
V will allways be the same.
=A0=A0=A0=A0You dont understand UP is a gain in mass .
You dont understand it isnt.
Where did you get a PHD ???????
Why are you asking this. You have fully identified who I am. Why would
you care.
=A0=A0The mass of a neutron changes mass at C wile in orbit . In an
energy slope it will have more mass at the top of the orbit than when at
the botom of the orbit.
So the neutron is more mass falling to the center of the atom when on
the top 1/2 of the atom than the bottom 1/2 and thats what pushes the
atom to less mass.
=A0=A0Do you understand how Einsteins gravity works ? =A0 Not many
physicsist
do.
=A0=A0=A0=A099.9 % of PHD's dont .
Ok. You are the exception to the rule I take it? No one else but you can
understand it...... Doesn't that tell you something.
By the way, going back to your previous threads where you were either
going to come round and kill me yourself or get your henchmen to do it;
its a nice sunny day outside here so I will (as planned) be sitting in
the garden waiting for you.
.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 12:26:28 PM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:27177-426BCB2D-82@storefull-3214.bay.webtv.net...
You gained mass when you got up on the chair.
You flunked basic physics.
Your a newbee here or anywhere in physics.
Up is a gain in mass and is basic physics .
---
It is not but you are welcome to belive this as long as you like. Up is not
a gain in mass - have you ever looked at the schema for ballistic missile
launches or plane take offs?
Probably not.
---
Your calling me dilusional ,,about the fact you are the only T Wake ..
you cant post 4 T Wake's if you include your self. So you call me
dilusional to try hiding the fact ..hay dumbass dont even try insisting
there are more than 1 T Wake unless you can prove it and dont try
DILLUSIONAL name calling I wount be intimadated. Your attmt to cover
your crap up by acting as stupid as moron max wount work .. You must
think I don't know what Im talking about and you think scocal
intimadation can make you look smart when you have no clue
---
I have no intention of trying to intimidate you - you are after all, the
richest 8 foot tall person on the Earth. Why would I try to intimidate you?
You do truly have no clue though. Visit this site and do a search for T WAKE
http://www.192.com/search/search.cfm
As you will see 125 records - all different. Feel free to ignore this and
carry on your ranting. I am sure with your wealth and engineering prowess
you have already looked through this and found better things to do.
Get a life.
---
Your twice busted ..you cant post 4 T Wakes .
You can't post any facts about physics because you don't know basic
physics.
---
I wish you couldnt post. Why did WebTV ever lower their already poor
standards to give you a subscription.
.
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| User: "yt56erd" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 12:19:56 PM |
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tj Frazir spews constant ***** onto the internet.
you dont know anything
you are a retard
there is only 1 tjFrazir on the world and he is a buck toothed gimp
tj dickwad frazir things up is more mass
what a *****
.
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 11:53:54 AM |
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You try intimadation ,, I let 5 dumbasses d it so you think you can.
Now your sitting in the garden ...bull.
Why would I know to pull the triger as soon as you resort to
intimadation DOC ???
Your empty post lack any facts.
Once more they defie basic physics.
Instead of reading Dr Einsteins work or any physics book ,,you try
proving a point by calling someone stupid and hope scocal depthpravation
works.
And now your waiting for me to waist 20 grand on you and have you
shot=A1=A1=A1=A1=A1
Your ego was the first casulty.
Now read the book stupid.
want me to find you a book ??
You a teacher !!!!!
shame on you ..
Do your students giggle allot ??
Physics is going to change the way you deal with people. The Games
people Play dont work here. The instant you try the games here you
became the hockey puck. I have a big stick " MOE " math on EVRYTHING .
I bet I did more math than anyone else alive.
And you still have not read the first book T Wake .
I know you did not read the first book cuz I just tested the first
book and you flunked it.
UP is a gain in mass MORON .
Read the book or stay a moron.
.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 12:33:31 PM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:27177-426BCF22-84@storefull-3214.bay.webtv.net...
You try intimadation ,, I let 5 dumbasses d it so you think you can.
Now your sitting in the garden ...bull.
Why would I know to pull the triger as soon as you resort to
intimadation DOC ???
---
I spent all day in the garden reading and watching my daughter play.
I even caught the sun a bit.
Prove I wasnt in my garden.
---
Your empty post lack any facts.
Once more they defie basic physics.
Instead of reading Dr Einsteins work or any physics book ,,you try
proving a point by calling someone stupid and hope scocal depthpravation
works.
---
Sadly, you have yet to have a post that contains any facts yet you never let
it stop you.
---
And now your waiting for me to waist 20 grand on you and have you
shot¡¡¡¡¡
Your ego was the first casulty.
---
You are the one who made the threat in the first place. I simply pointed out
you are living in a fantasy world and there was no risk to me whatsoever.
---
Now read the book stupid.
want me to find you a book ??
You a teacher !!!!!
---
Why do you think I am a teacher?
---
shame on you ..
Do your students giggle allot ??
Physics is going to change the way you deal with people. The Games
people Play dont work here. The instant you try the games here you
became the hockey puck. I have a big stick " MOE " math on EVRYTHING .
I bet I did more math than anyone else alive.
And you still have not read the first book T Wake .
I know you did not read the first book cuz I just tested the first
book and you flunked it.
UP is a gain in mass MORON .
Read the book or stay a moron.
---
Up is not a gain in mass. Please, tj stop making yourself look even more
foolish than normal.
Mass is not weight.
Gravity is the weakest force and its strength diminishes in relation to the
distance between the objects.
.
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 01:23:40 PM |
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I know mass is not weight dumbass .
ITs in 1 G dumbass .
Any gain in mass will be a gain in weight .
IF I heat it up 5 deg did it gain mass and and will it allso weight
more ??? idiot.
Place 100 lb on a scale at SL .. then elevate it 1000 feet ..now it
weighs 100.002 pounds.
Place the 100 lb at SL on the scale and heat it up till it wieghs
100.002 lb.
heat is allso mass.
.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 01:52:01 PM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:8352-426BE42C-1@storefull-3218.bay.webtv.net...
I know mass is not weight dumbass .
So why did you say that you could measure the gain in mass with scales?
ITs in 1 G dumbass .
Any gain in mass will be a gain in weight .
Yes. This doesnt imply the opposite is also true though.
IF I heat it up 5 deg did it gain mass and and will it allso weight
more ??? idiot.
If you heat what up? This is a pretty random question. If you have a bucket
of water at 368 kelvin and you increase it by 5 kelvin it will lose mass.
What has that got to do with gravity?
Do you realise there are four fundamental forces?
Place 100 lb on a scale at SL .. then elevate it 1000 feet ..now it
weighs 100.002 pounds.
This is proof (if required) you are failing to differentiate between mass
and weight.
Place the 100 lb at SL on the scale and heat it up till it wieghs
100.002 lb.
heat is allso mass.
Heat is energy (IIRC mostly potential energy but I could be wrong), energy
and mass is interchangeable so in some respects you have a point here -
however its irrelevant and presents a false image. If you heat something up
eventually the mass of the original object decreases as its component parts
change into other forms.
Still cant see what heating things up has got to do with gravity.
.
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| User: "bz" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 03:34:19 PM |
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"T Wake" <taswakeAt@hotmail.com> wrote in
news:IOSdnUD-Yfp3d_bfRVnyuw@pipex.net:
"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:8352-426BE42C-1@storefull-3218.bay.webtv.net...
Place the 100 lb at SL on the scale and heat it up till it wieghs
100.002 lb.
heat is allso mass.
Well, lets see if this is possible. 0.002 lb mass equivalent is 8.1e13
Joules.
if the mass were iron, and its heat capacity was 470 Joule/(kg K)
you would have to raise the 100 lb mass to 3.8e9 degrees K
(assuming you started at zero).
I think the 100 lbs just went up in smoke.
On the other hand, if we just heat 100 lb of iron to 1000 deg K
it would gain 5e-10 lb. That represents 5 parts per /1,000,000,000,000
I would have a hard time measuring that. Maybe you have a better balance
than I do.
--
bz
please pardon my infinite ignorance, the set-of-things-I-do-not-know is an
infinite set.
bz+sp@ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 03:54:49 PM |
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"bz" <bz+sp@ch100-5.chem.lsu.edu> wrote in message
news:Xns96429E67A159AWQAHBGMXSZHVspammote@130.39.198.139...
<snip relevant mathematics for brevity>
I would have a hard time measuring that. Maybe you have a better balance
than I do.
Balance is sadly missing in tj Frazir's life.
.
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| User: "tj Frazir" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
24 Apr 2005 06:02:12 PM |
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BZ ,,get out the ballance beem and lets measure 100 deg in a small 1
pound block.
The two are oposit on the ballance beam in perfect ballance ..
then you heat one up just a bit and the mass of the heat will push at
side down.
Now what mass of 002 pounds is 13 jl ?
ya got it from petrolium stupid I reconsise the math and your allways
doing the wrong math.
Your still using ladderal math on falling pipes.
Yer math is a joke.
Then you lie and try to cheet math !
.
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| User: "T Wake" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
25 Apr 2005 04:04:31 AM |
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:4084-426C2574-464@storefull-3212.bay.webtv.net...
BZ ,,get out the ballance beem and lets measure 100 deg in a small 1
pound block.
The two are oposit on the ballance beam in perfect ballance ..
then you heat one up just a bit and the mass of the heat will push at
side down.
Now what mass of 002 pounds is 13 jl ?
ya got it from petrolium stupid I reconsise the math and your allways
doing the wrong math.
Your still using ladderal math on falling pipes.
Yer math is a joke.
Then you lie and try to cheet math !
tj - bz pointed out the correct measurements. Your messages are becoming
even more incoherent now.
You lie constantly and the only reason you don't try to cheat mathematics is
that you make your own version of mathematics / formula up.
.
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| User: "bz" |
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| Title: Re: This Week's Finds in Mathematical Physics Louis |
25 Apr 2005 08:30:27 AM |
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"T Wake" <taswakeAt@hotmail.com> wrote in news:ntidnbXMit4
_L_HfRVnygQ@pipex.net:
"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:4084-426C2574-464@storefull-3212.bay.webtv.net...
BZ ,,get out the ballance beem and lets measure 100 deg in a small 1
pound block.
assuming an iron block of 1 lb, heated by 100 deg:
it would weigh 1.0000000000005236 lb
BTW, you will need to do your weighing in a vacuum because air currents due
to convection will upset the balance. The hot air around the iron weight
would be in motion, trying to lift the hot item and the hot air will be less
dense, this reduces the boyance of the object, making it seem heavier. The
twe effects will probably come close to cancelling each other, but to be
safe, do your weighing in your vacuum chamber.
Best to work with two identical 1 lb masses. Your standard mass set will, of
course, need to be recalibrated for vacuum work.
The two are oposit on the ballance beam in perfect ballance ..
then you heat one up just a bit and the mass of the heat will push at
side down.
Now what mass of 002 pounds is 13 jl ?
13 joules is the energy equivalent of a mass that represents 0.00000000001.6%
of 0.002 lb.
ya got it from petrolium stupid I reconsise the math and your allways
doing the wrong math.
I got it from E=mc^2. Nothing to do with petrolium
Your still using ladderal math on falling pipes.
A pipe doesn't care whether it is horizontal or vertical, If the fluid is
flowing through it, there is friction. When there is friction, there is loss
of head. Just like the IR drop when current flows through a resistor.
You neglected the friction in your calculations and presented the figures as
if they were taken from the real world. Because you neglected the friction,
your pipe size was too small.
It is an easy mistake to make, if you are just throwing out numbers.
You made a similar mistake when you claimed that transmission line losses
would increase the current in the line.
If you increase the voltage applied to the line to whatever is needed to
overcome the IR drop, the load will see the proper voltage and current. This
is dangerous, however, because when you switch off the load, the voltage at
the load end of the line will jump up to the generator's voltage.
The above, of course, assumes that the transmission line is NOT leaky and
there are no other loads on the line.
Yer math is a joke.
I don't joke about math. I do play with words, sometimes.
Then you lie and try to cheet math !
I neither lie, nor call people stupid. I don't need to do so.
Insults are the refuge of those who have nothing better to say.
--
bz
please pardon my infinite ignorance, the set-of-things-I-do-not-know is an
infinite set.
bz+sp@ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
.
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| User: "tj Frazir" |
|
| Title: Re: This Week's Finds in Mathematical Physics Louis |
25 Apr 2005 05:33:47 PM |
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wrong again.
Its done all the time.
two identical steel blocks a few pounds each are placed on the ballance
ad a buson burner heats on and in a few minutes the hot one pushes that
side down.
Its done in classes evry day.
.
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| User: "T Wake" |
|
| Title: Re: This Week's Finds in Mathematical Physics Louis |
25 Apr 2005 06:03:20 PM |
|
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"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:23292-426D704B-571@storefull-3216.bay.webtv.net...
wrong again.
Its done all the time.
two identical steel blocks a few pounds each are placed on the ballance
ad a buson burner heats on and in a few minutes the hot one pushes that
side down.
Its done in classes evry day.
tj Frazir - it is nice that you have found a friend here to talk to however
there are some problems with this experiment and how it relates to
everything else you post.
For a start is it done in a vacuum?
Most importantly, what has this got to do with your flawed understanding of
gravity?
.
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| User: "bz" |
|
| Title: Re: This Week's Finds in Mathematical Physics Louis |
25 Apr 2005 08:00:18 PM |
|
|
"T Wake" <taswakeAt@hotmail.com> wrote in
news:D86dnR_RL4Kh6vDfRVnyhQ@pipex.net:
"tj Frazir" <GravityPhysics@webtv.net> wrote in message
news:23292-426D704B-571@storefull-3216.bay.webtv.net...
wrong again.
Its done all the time.
two identical steel blocks a few pounds each are placed on the ballance
ad a buson burner heats on and in a few minutes the hot one pushes that
side down.
Its done in classes evry day.
Ya know, it is strange, I looked with google for such an experiment.
If it is done in classes every day, you would think google would show it.
I can't find such an experiment anywhere.
--
bz
please pardon my infinite ignorance, the set-of-things-I-do-not-know is an
infinite set.
bz+sp@ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
.
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| User: "T Wake" |
|
| Title: Re: This Week's Finds in Mathematical Physics Louis |
26 Apr 2005 04:21:30 AM |
|
|
"bz" <bz+sp@ch100-5.chem.lsu.edu> wrote in message
news:Xns9643CB80E8B85WQAHBGMXSZHVspammote@130.39.198.139...
Ya know, it is strange, I looked with google for such an experiment.
If it is done in classes every day, you would think google would show it.
I can't find such an experiment anywhere.
Well I don't ever remember doing it in class, even 30 years ago - however I
thought that maybe other countries did things differently.
Working on the, very flawed, assumption that tj Frazir is actually telling
the truth here there are a few possibilities as to why. Sadly, tj Frazir
fails to appreciate the need to control his experiments and makes the simple
assumption that doing it has resulted in an increase in mass.
Oh well. I can see why you have him killfiled.
.
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| User: "tj Frazir" |
|
| Title: Re: This Week's Finds in Mathematical Physics Louis |
26 Apr 2005 10:13:30 AM |
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heat is mass and yer a dumbass.
Dr Julian Summers did it on his show.
You can do it . Its a classic and you retarted fuckers think BZ did the
math corect but he did not.
What was wrong with his math,,do you have a clue ?
last time he did the wrong math he did ladderal pipe math instead of a
falling pipe.
Now he does the wrong math again and you morons said it was corect
because your stupid.
Then you never saw the first leson in thermal mass on the ballance
beam.
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